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Netlab Reference Manual evidence
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<H1> evidence
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<h2>
Purpose
</h2>
Re-estimate hyperparameters using evidence approximation.

<p><h2>
Synopsis
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<PRE>
[net] = evidence(net, x, t)
[net, gamma, logev] = evidence(net, x, t, num)
</PRE>


<p><h2>
Description
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<CODE>[net] = evidence(net, x, t)</CODE> re-estimates the
hyperparameters <CODE>alpha</CODE> and <CODE>beta</CODE> by applying Bayesian
re-estimation formulae for <CODE>num</CODE> iterations. The hyperparameter
<CODE>alpha</CODE> can be a simple scalar associated with an isotropic prior
on the weights, or can be a vector in which each component is
associated with a group of weights as defined by the <CODE>index</CODE>
matrix in the <CODE>net</CODE> data structure. These more complex priors can
be set up for an MLP using <CODE>mlpprior</CODE>. Initial values for the iterative
re-estimation are taken from the network data structure <CODE>net</CODE>
passed as an input argument, while the return argument <CODE>net</CODE>
contains the re-estimated values.

<p><CODE>[net, gamma, logev] = evidence(net, x, t, num)</CODE> allows the re-estimation 
formula to be applied for <CODE>num</CODE> cycles in which the re-estimated
values for the hyperparameters from each cycle are used to re-evaluate
the Hessian matrix for the next cycle.  The return value <CODE>gamma</CODE> is
the number of well-determined parameters and <CODE>logev</CODE> is the log
of the evidence.

<p><h2>
See Also
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<CODE><a href="mlpprior.htm">mlpprior</a></CODE>, <CODE><a href="netgrad.htm">netgrad</a></CODE>, <CODE><a href="nethess.htm">nethess</a></CODE>, <CODE><a href="demev1.htm">demev1</a></CODE>, <CODE><a href="demard.htm">demard</a></CODE><hr>
<b>Pages:</b>
<a href="index.htm">Index</a>
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<p>Copyright (c) Ian T Nabney (1996-9)


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